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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.216', 'a10': [-0.663581634584641, -0.7481038793122088], 'a2': [-0.97858746968012, 0.20583139747147455], 'a3': [-0.6393879136855247, -0.7688843188886557], 'a4': [0.9152668716298797, -0.4028480528646667], 'a5': [0.4953894057817187, 0.8686710174969784], 'a6': [0.7839575344483235, 0.6208144522977099], 'a7': [-0.4246245908531884, -0.9053695139791059], 'a8': [-0.8127499143005265, 0.5826127159653203], 'a9': [-0.1823661916657439, 0.9832306810394665], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.216', 'coeff_info': ['x^394 - 1', '0.999872846566010 + 0.0159464949121641*I', '\\\\zeta_{394}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.1029', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^184', 'a^252', 'a^368', 'a^66', 'a^42', 'a^268', 'a^158', 'a^110', 'a^250', 'a^95', 'a^226', 'a^202', 'a^58', 'a^318', 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'0.245659820729699519368650792688+0.969356101997120506238455486196*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(394)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.573815922330338239384715684203+0.0382619708230499633437900398080*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.843954596735', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.62143617333', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.51439646721', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.216', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/216'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-4729-4729.216-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-4729-4729.216-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': 0.21049769326340026, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.843954596735', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.216', 'Lhash_array': ['dirichlet_L_4729.216'], 'factors': ['1-4729-4729.216-r0-0-0'], 'label': '1-4729-4729.216-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/216'}
Lfunction data - 1-4729-4729.216-r0-0-0